One important thing to note is that the sawtooth function \(t - \left\lfloor \frac{t}{ \Delta } \right\rfloor \Delta \)  is not constant like in a constant delay model and increases linearly within an updating interval. Thus, if we interpret the update as a delay in information, then the delay that the customer experiences is non-stationary and is not constant. This is an important distinction from the constant delay models studied in [1]}, [2]} and the non-stationary behavior of the periodic updates will add additional complexities to our analysis of the updating model. We will also show that we cannot rely on previous analytical methods that were developed in [3]} for the constant delay setting because of the non-stationarity of the delay function. Non-stationary delay FDE models have been explored in the dynamical systems and control theory literature, see for example [4]}, [5]}, [6]}. However, much of this literature focuses on either looking at the average variation of the time varying function or providing robust bounds for stability with a non-stationary delay function.
